The former England midfielder will team up with his father for the second time in his career. The Saints manager gave Jamie his league debut for Bournmouth before selling him to Liverpool in 1991.
The 31-year-old who had six months remaining on his Tottenham contract asked for permission to leave despite turning down a similar move to Portsmouth in the summer.
"At this stage in my career I want to be playing more so I had a chat with Frank, Martin and the chairman and asked them to let me go they were great about it," he said.
In Spurs last four Premiership games the 31-year-old only appeared twice as a substitute, which included the final three minutes at White Hart Lane on New Year's Day.
There's no bitterness between the player and Martin Jol who has left Redknapp out the side since replacing Jacques Santini as head coach.
"Martin said when I finish playing to come and talk to him about a coaching role," he added.
Redknapp goes straight into the squad to face Fulham at St Mary’s tonight.